Surface Extrema

Maxima

mountain peak or summit or top

ridge

plateau, high plane

Minima

deep, hole, depression, hollow

valley

plain, low plane

Example Earth

planes with elevation of their kind under and over water level

having ranges and abysses as borders, depressions and heights as land marks

Surface Survey

Assuming a net of measure points all over the globe, we can connect each point with it’s nearest neighbours by arrows, which direct down hill, the direction of the rain fall water flow.

The more points we set, the more accurate our model of peaks, ridges, valleys and hollows will become.

Arrow Cross

maximum: all arrows direct away

minimum: all arrows meet

saddle point: two opposite arrows meet and the orthogonal arrows direct away, a valley crossing a ridge?

ridge point:

valley point: